While Republicans in the Senate have announced plans for bipartisan hearings on health care beginning when Congress returns to work after Labor Day, the White House is making clear that President Donald Trump continues to look for more immediate answers on a GOP health care bill that would involve getting only a majority of Republican votes in the Senate, as he meets Wednesday afternoon with one key GOP lawmaker, Sen. Rob Portman of Ohio.

Portman has made clear to reporters in recent days that while last week's defeat of the GOP 'skinny' bill was a setback, he's not ready to give up on the GOP figuring out how to get to 50 votes in the Senate.

"I think we should be working together and I think that's a way to see if we can put the pieces back together on legislation that makes sense," Portman said this week - and he arrives at a White House today that has not given up on the GOP bill.

As the sun rose on Wednesday, it still wasn't clear what the President would do about the next round of scheduled payments to insurance companies, known as CSR's - or Cost Sharing Reductions - which help lower-income Americans afford health insurance through the Obama health law exchanges.

"We’re continuing to try to push a new healthcare system," incoming White House Press Secretary Sarah Huckabee Sanders told reporters on Tuesday. "We know that Obamacare is failing. We know that inaction is simply not okay."

"I like the idea that we're not quitting," said Sen. Lindsey Graham (R-SC), who met with the President in recent days about his idea to include a different formula on block grants to the states that would cover health care money.

Other Republicans agreed that the White House shouldn't give up on the GOP health care bill, which was just one vote short of victory.

"I think the President is frustrated," Sen. Mike Rounds (R-ND) said of the lack of final action by the Senate on health. "I happen to agree that we should move forward."

But while the President was pushing for a GOP-only health care bill, top Republicans were already shifting into a different mode, setting bipartisan hearings for after Labor Day in a key Senate committee.

“We will hear from state insurance commissioners, patients, governors, health care experts and insurance companies,” said Sen. Lamar Alexander (R-TN), who chairs the main Senate panel that deals with health policy matters.

“For the short term, the proposal is by mid-September to see if we can agree on a way to stabilize the individual insurance market,” Alexander added.

On the Senate floor, there was no indication of any plan by Republican leaders to hold a new vote on health care; for now, they remain one vote short, as few on Capitol Hill believe there is a chance that any of the three "No" votes will flip anytime soon - Sen. John McCain (R-AZ), Sen. Lisa Murkowski (R-AK), and Sen. Susan Collins (R-ME).

Collins made clear on Tuesday that she was all for the new round of bipartisan hearings in September, and not a rush to simply change the existing GOP health bill.

"I'm very excited about that," Collins said of the post-Labor Day hearings. "I believe that's the direction we should have gone in, in the first place."

"Good news," McCain tweeted on Wednesday morning about the decision to hold hearings, saying the decision "may be a step in the right direction."

The current plan is to have the Senate work through next week, and then go home for a three week summer break - without a new Senate vote on the health care issue.

By Tuesday evening, the Senate had already achieved two of those goals stated by Majority Leader Mitch McConnell, confirming the new FBI Director, and approving a VA choice bill. Also, a big batch of military nominees were confirmed on Monday.

Notable for not being on that priority list in August was the health care issue, which might not be the preference for the President.

"We want to continue to make (health care legislation) a priority. We want to work with Congress to do that," said Sanders.